(B) Consider a small element of length $dx$ at a distance $x$ from the free end of the rubber cord.The weight of the portion below this element is $W

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

(B) Consider a small element of length $dx$ at a distance $x$ from the free end of the rubber cord.The weight of the portion below this element is $W = (A \cdot x \cdot D) \cdot g$.The stress at this section is $\sigma = \frac{W}{A} = x D g$.By Hooke's Law,the strain is $\epsilon = \frac{\sigma}{E} = \frac{x D g}{E}$.The extension of the small element $dx$ is $dl = \epsilon dx = \frac{x D g}{E} dx$.To find the total extension $l$,we integrate from $x = 0$ to $x = L$:$l = \int_{0}^{L} \frac{D g}{E} x dx = \frac{D g}{E} \left[ \frac{x^2}{2} \right]_{0}^{L} = \frac{L^2 D g}{2 E}$.

Class 11 Physics Mechanical Properties of Solids Young’s Modulus

Difficult

An Indian rubber cord $L$ metre long and area of cross-section $A$ $m^2$ is suspended vertically. The density of rubber is $D$ $kg/m^3$ and Young's modulus of rubber is $E$ $N/m^2$. If the wire extends by $l$ metre under its own weight,then the extension $l$ is:

A
$L^2Dg/E$
B
$L^2Dg/2E$
C
$L^2Dg/4E$
D
$L$

Explore More

Browse All

Question Bank

All Subjects

Class 11 Questions

Class 11

Physics Questions

Chapter

Mechanical Properties of Solids

Subtopic

Young’s Modulus

$A$ pendulum made of a uniform wire of cross-sectional area $A$ has a time period $T$. When an additional mass $M$ is added to its bob,the time period changes to $T_M$. If the Young's modulus of the material of the wire is $Y$,then $\frac{1}{Y}$ is equal to ($g$ = gravitational acceleration).

DifficultJEE MAIN 2015

View Solution

Two copper wires $A$ and $B$ of lengths in the ratio $1: 2$ and diameters in the ratio $3: 2$ are stretched by forces in the ratio $3: 1$. The ratio of the elastic potential energies stored per unit volume in the wires $A$ and $B$ is

EasyAP EAMCET 2024

View Solution

The adjacent graph shows the extension $(\Delta l)$ of a wire of length $1\, m$ suspended from the top of a roof at one end and with a load $W$ connected to the other end. If the cross-sectional area of the wire is $10^{-6}\, m^2$,calculate the Young's modulus of the material of the wire.

MediumIIT 2003

View Solution

$A$ wire is stretched by $0.01 \ m$ by a certain force $F$. Another wire of the same material whose diameter and length are double that of the original wire is stretched by the same force. Then its elongation will be (in $m$)

Medium

View Solution

$A$ thick metal wire of density $\rho$ and length $L$ is hung from a rigid support. The increase in length of the wire due to its own weight is ($Y =$ Young's modulus of the material of the wire).

MediumKCET 2024

View Solution

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial

For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free

For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo

An Indian rubber cord $L$ metre long and area of cross-section $A$ $m^2$ is suspended vertically. The density of rubber is $D$ $kg/m^3$ and Young's modulus of rubber is $E$ $N/m^2$. If the wire extends by $l$ metre under its own weight,then the extension $l$ is:

Similar Questions

$A$ pendulum made of a uniform wire of cross-sectional area $A$ has a time period $T$. When an additional mass $M$ is added to its bob,the time period changes to $T_M$. If the Young's modulus of the material of the wire is $Y$,then $\frac{1}{Y}$ is equal to ($g$ = gravitational acceleration).

Two copper wires $A$ and $B$ of lengths in the ratio $1: 2$ and diameters in the ratio $3: 2$ are stretched by forces in the ratio $3: 1$. The ratio of the elastic potential energies stored per unit volume in the wires $A$ and $B$ is

The adjacent graph shows the extension $(\Delta l)$ of a wire of length $1\, m$ suspended from the top of a roof at one end and with a load $W$ connected to the other end. If the cross-sectional area of the wire is $10^{-6}\, m^2$,calculate the Young's modulus of the material of the wire.

$A$ wire is stretched by $0.01 \ m$ by a certain force $F$. Another wire of the same material whose diameter and length are double that of the original wire is stretched by the same force. Then its elongation will be (in $m$)

$A$ thick metal wire of density $\rho$ and length $L$ is hung from a rigid support. The increase in length of the wire due to its own weight is ($Y =$ Young's modulus of the material of the wire).

Vedclass Test Series

Exam Paper Generator

Online Exam Module